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question; we must, however, know the amount we need at the end (FV), the interest rate (I), and the
length of time (N). The formula for present value is:
(Formula 4b)
We previously solved for future value: N = 10 years, interest (I) = 5%, and present value (P V) =
$50. Our result was $81.44. We used formula 4a to solve for FV: F V = P V × (1 + I) N . Note the
similarities in the two formulas. Using the rules of algebra, we change formula 4a to 4b and now solve
for PV.
Note that the $50.00 was the initial amount deposited into Billy‟s account on his 10th birthday by
his aunt. (When using financial calculators or Excel, the PV will result in a negative number; this
represents the cash outflow or deposit required to result in a positive FV.)
PV Exercises
The following exercise illustrates solving for PV using algebra and Excel.
Find the PV, the amount we need to deposit today into a savings account that pays a fixed interest
rate of 7% over the term of the deposit, which will result in a FV of $8,000 at the end of five years.
P V = Present value (unknown)
F V = $8,000
I = 7%
N = 5 years
Using Formula 4b and substituting given values,
The values in Exhibit 4.6 reflect these calculations.
Here is a step-by-step Excel approach to finding the PV of $8,000 (see Exhibit 4.7).
• Enter the following values into cells C4, C5, and C6, respectively.
C4 = $8,000 (Note that this not a negative value, as this is the FV.)
C5 = 7%